LEADER 03503nam 22005655 450 001 9910255455703321 005 20200701155046.0 010 $a3-319-71306-X 024 7 $a10.1007/978-3-319-71306-9 035 $a(CKB)4100000001794754 035 $a(DE-He213)978-3-319-71306-9 035 $a(MiAaPQ)EBC5247432 035 $a(PPN)223955612 035 $a(EXLCZ)994100000001794754 100 $a20180125d2017 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Geometric Hopf Invariant and Surgery Theory /$fby Michael Crabb, Andrew Ranicki 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XVI, 397 p. 1 illus. in color.) 225 1 $aSpringer Monographs in Mathematics,$x1439-7382 311 $a3-319-71305-1 320 $aIncludes bibliographical references and index. 327 $a1 The difference construction -- 2 Umkehr maps and inner product spaces -- 3 Stable homotopy theory -- 4 Z_2-equivariant homotopy and bordism theory -- 5 The geometric Hopf invariant -- 6 The double point theorem -- 7 The -equivariant geometric Hopf invariant -- 8 Surgery obstruction theory -- A The homotopy Umkehr map -- B Notes on Z2-bordism -- C The geometric Hopf invariant and double points (2010) -- References -- Index. 330 $aWritten by leading experts in the field, this monograph provides homotopy theoretic foundations for surgery theory on higher-dimensional manifolds. Presenting classical ideas in a modern framework, the authors carefully highlight how their results relate to (and generalize) existing results in the literature. The central result of the book expresses algebraic surgery theory in terms of the geometric Hopf invariant, a construction in stable homotopy theory which captures the double points of immersions. Many illustrative examples and applications of the abstract results are included in the book, making it of wide interest to topologists. Serving as a valuable reference, this work is aimed at graduate students and researchers interested in understanding how the algebraic and geometric topology fit together in the surgery theory of manifolds. It is the only book providing such a wide-ranging historical approach to the Hopf invariant, double points and surgery theory, with many results old and new. . 410 0$aSpringer Monographs in Mathematics,$x1439-7382 606 $aAlgebraic topology 606 $aManifolds (Mathematics) 606 $aComplex manifolds 606 $aAlgebraic Topology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28019 606 $aManifolds and Cell Complexes (incl. Diff.Topology)$3https://scigraph.springernature.com/ontologies/product-market-codes/M28027 615 0$aAlgebraic topology. 615 0$aManifolds (Mathematics). 615 0$aComplex manifolds. 615 14$aAlgebraic Topology. 615 24$aManifolds and Cell Complexes (incl. Diff.Topology). 676 $a514.24 700 $aCrabb$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut$0767648 702 $aRanicki$b Andrew$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910255455703321 996 $aThe Geometric Hopf Invariant and Surgery Theory$92044176 997 $aUNINA